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Dive into Theorem 10.6 involving Inscribed Angle Theorem, explore proofs, dissect Case 1 applications, and solve real-world examples in Theorem 10.7 & 10.8. Learn to use Inscribed Angles to find measures and embrace Algebra for angle challenges. Reveal the mysteries of inscribed triangles in Theorem 10.9 and wrap up with practical examples. Unravel the essence of angles inscribed in polygons, intercepted arcs, and circle geometry concepts.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 10–3) CCSS Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle Theorem (Case 1) Example 1: Use Inscribed Angles to Find Measures Theorem 10.7 Example 2: Use Inscribed Angles to Find Measures Example 3: Use Inscribed Angles in Proofs Theorem 10.8 Example 4: Find Angle Measures in Inscribed Triangles Theorem 10.9 Example 5: Real-World Example: Find Angle Measures Lesson Menu

  3. A. 60 B. 70 C. 80 D. 90 5-Minute Check 1

  4. A. 40 B. 45 C. 50 D. 55 5-Minute Check 2

  5. A. 40 B. 45 C. 50 D. 55 5-Minute Check 3

  6. A. 40 B. 30 C. 25 D. 22.5 5-Minute Check 4

  7. A. 24.6 B. 26.8 C. 28.4 D. 30.2 5-Minute Check 5

  8. A. B. C. D. 5-Minute Check 6

  9. Content Standards G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Mathematical Practices 7 Look for and make use of structure. 3 Construct viable arguments and critique the reasoning of others. CCSS

  10. You found measures of interior angles of polygons. • You found the measures of central angles. • Find measures of inscribed angles. • Find measures of angles of inscribed polygons. Then/Now

  11. inscribed angle • intercepted arc Vocabulary

  12. Concept

  13. Concept

  14. Use Inscribed Angles to Find Measures A. Find mX. Answer:mX = 43 Example 1

  15. B. Use Inscribed Angles to Find Measures = 2(52) or 104 Example 1

  16. A. Find mC. A. 47 B. 54 C. 94 D. 188 Example 1

  17. B. A. 47 B. 64 C. 94 D. 96 Example 1

  18. Concept

  19. RS R and S both intercept . Use Inscribed Angles to Find Measures ALGEBRA Find mR. mRmS Definition of congruent angles 12x – 13 = 9x + 2 Substitution x = 5 Simplify. Answer:So, mR = 12(5) – 13 or 47. Example 2

  20. ALGEBRA Find mI. A. 4 B. 25 C. 41 D. 49 Example 2

  21. Concept

  22. Find Angle Measures in Inscribed Triangles ALGEBRA Find mB. ΔABC is a right triangle because C inscribes a semicircle. mA + mB + mC = 180Angle Sum Theorem (x + 4) + (8x – 4) + 90 = 180 Substitution 9x + 90 = 180 Simplify. 9x = 90 Subtract 90 from each side. x = 10 Divide each side by 9. Answer:So, mB = 8(10) – 4 or 76. Example 4

  23. ALGEBRA Find mD. A. 8 B. 16 C. 22 D. 28 Example 4

  24. Concept

  25. Find Angle Measures INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mS and mT. Example 5

  26. Find Angle Measures Since TSUV is inscribed in a circle, opposite angles are supplementary. mS + mV = 180 mU + mT = 180 mS + 90= 180 (14x) + (8x + 4) = 180 mS = 90 22x + 4 = 180 22x = 176 x = 8 Answer:So, mS = 90 and mT = 8(8) + 4 or 68. Example 5

  27. INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mN. A. 48 B. 36 C. 32 D. 28 Example 5

  28. End of the Lesson

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